This is a proposal for extensions of an extant statistical technology so that it becomes directly applicable to Phase I of the Human Brian Project. Integration and analysis of neuroscientific information require a facility for the biometric standardization of gross brain shape. This standardization is required for achieving such aims as averaging brain images over homogeneous patient or normal samples, referring histological or ultrastructural measurements to a macroscopic coordinate system, and evaluating the correlation of structure with function in health or in disease. The present proposal will construct a comprehensive algebraic- geometric framework for that standardization of brain shape. The proposed work builds on modern techniques of morphometrics, the statistics of biological shape and shape change. These techniques all presume the existence of landmarks, points, such as "Anterior Commissure," with biological identities as well as geometric locations. Configurations of landmarks both serve as multivariate data themselves, as for averaging of shape or its correlation with causes or effects, and drive a canonical interpolation map, the thin-plate spline, which serves to standardize the geometry of any subsequent image processing, averaging, and analysis. In the past year techniques have been introduced that extend these strengths of the landmark-driven spline to incorporate information from edge-directions and other important aspects of the local structure of these images. To date this work has emphasized two-dimensional images. We propose to extend the new differential techniques to handle the three-dimensional structures, such as tracts, lobes, and gyri, that are crucial for the representation of neuroanatomical variability at the gross level. We propose to supply the Human Brain Project with an analytically uniform set of algorithms for standardization of their clinical images across sites and projects. We will enumerate the types of descriptors required, supply algorithmic parameterizations as necessary, and generate a consistent set of three-dimensional warping facilities for the uniform representation of these aspects of geometry across all the laboratories of the Project, whatever the precision or scale of the relevant measurements. We will further supply a mathematical basis for the intercomparison of the many earlier versions of these computations, both superposition techniques and "deformable template" analyses, that have been previously developed by many other neuroscientists. Finally, we will serve as a test site for the new approaches to more sophisticated neuroscientific visualizations, such as structure-function correlations, that the standardizations make possible. The new methods should optimize the geometric efficiency and statistical power with which the Human Brain Project will eventually exploit the massive archives of data it intends to assemble for diverse scientific and clinical purposes.